

import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput





def 	__a     (      A__			:  int			,  A__			:  List[Any]=0.9_9_9			,  A__			:  Any="cosine"			,  ):





    if alpha_transform_type == "cosine":

        def alpha_bar_fn(A__			:  Tuple       ):
            return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2       ) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(A__			:  str       ):
            return math.exp(t * -1_2.0       )

    else:
        raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"       )

    SCREAMING_SNAKE_CASE										=   []
    for i in range(A_       ):
        SCREAMING_SNAKE_CASE										=   i / num_diffusion_timesteps
        SCREAMING_SNAKE_CASE										=   (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar_fn(A_       ) / alpha_bar_fn(A_       )			,  A_       )       )
    return torch.tensor(A_			,  dtype=torch.floataa       )





class 			_SCREAMING_SNAKE_CASE (   _A					,       _A		):







   '''simple docstring'''




   lowerCamelCase__				=      [e.name for e in KarrasDiffusionSchedulers]
   lowerCamelCase__				=      2





   @register_to_config
   def __init__(       self					:			Optional[Any]     , __lowerCamelCase					:			int = 1000     , __lowerCamelCase					:			float = 0.00_085     , __lowerCamelCase					:			float = 0.012     , __lowerCamelCase					:			str = "linear"     , __lowerCamelCase					:			Optional[Union[np.ndarray, List[float]]] = None     , __lowerCamelCase					:			str = "epsilon"     , __lowerCamelCase					:			str = "linspace"     , __lowerCamelCase					:			int = 0     , ):






       if trained_betas is not None:
           SCREAMING_SNAKE_CASE										=   torch.tensor(UpperCamelCase__     , dtype=torch.floataa			)
       elif beta_schedule == "linear":
           SCREAMING_SNAKE_CASE										=   torch.linspace(UpperCamelCase__     , UpperCamelCase__     , UpperCamelCase__     , dtype=torch.floataa			)
       elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           SCREAMING_SNAKE_CASE										=   (
               torch.linspace(beta_start**0.5     , beta_end**0.5     , UpperCamelCase__     , dtype=torch.floataa			) ** 2
           )
       elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           SCREAMING_SNAKE_CASE										=   betas_for_alpha_bar(UpperCamelCase__			)
       else:
           raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"			)

       SCREAMING_SNAKE_CASE										=   1.0 - self.betas
       SCREAMING_SNAKE_CASE										=   torch.cumprod(self.alphas     , dim=0			)

       #  set all values
       self.set_timesteps(UpperCamelCase__     , UpperCamelCase__     , UpperCamelCase__			)





   def      _snake_case		(       self					:			int     , __lowerCamelCase					:			Any     , __lowerCamelCase					:			Tuple=None			):






       if schedule_timesteps is None:
           SCREAMING_SNAKE_CASE										=   self.timesteps

       SCREAMING_SNAKE_CASE										=   (schedule_timesteps == timestep).nonzero()

       # The sigma index that is taken for the **very** first `step`
       # is always the second index (or the last index if there is only 1)
       # This way we can ensure we don't accidentally skip a sigma in
       # case we start in the middle of the denoising schedule (e.g. for image-to-image)
       if len(self._index_counter			) == 0:
           SCREAMING_SNAKE_CASE										=   1 if len(UpperCamelCase__			) > 1 else 0
       else:
           SCREAMING_SNAKE_CASE										=   timestep.cpu().item() if torch.is_tensor(UpperCamelCase__			) else timestep
           SCREAMING_SNAKE_CASE										=   self._index_counter[timestep_int]

       return indices[pos].item()





   @property
   def      _snake_case		(       self					:			int			):






       if self.config.timestep_spacing in ["linspace", "trailing"]:
           return self.sigmas.max()

       return (self.sigmas.max() ** 2 + 1) ** 0.5





   def      _snake_case		(       self					:			Dict     , __lowerCamelCase					:			torch.FloatTensor     , __lowerCamelCase					:			Union[float, torch.FloatTensor]     , ):
       SCREAMING_SNAKE_CASE										=   self.index_for_timestep(UpperCamelCase__			)

       if self.state_in_first_order:
           SCREAMING_SNAKE_CASE										=   self.sigmas[step_index]
       else:
           SCREAMING_SNAKE_CASE										=   self.sigmas_interpol[step_index]

       SCREAMING_SNAKE_CASE										=   sample / ((sigma**2 + 1) ** 0.5)
       return sample





   def      _snake_case		(       self					:			List[str]     , __lowerCamelCase					:			int     , __lowerCamelCase					:			Union[str, torch.device] = None     , __lowerCamelCase					:			Optional[int] = None     , ):
       SCREAMING_SNAKE_CASE										=   num_inference_steps

       SCREAMING_SNAKE_CASE										=   num_train_timesteps or self.config.num_train_timesteps

       # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
       if self.config.timestep_spacing == "linspace":
           SCREAMING_SNAKE_CASE										=   np.linspace(0     , num_train_timesteps - 1     , UpperCamelCase__     , dtype=UpperCamelCase__			)[::-1].copy()
       elif self.config.timestep_spacing == "leading":
           SCREAMING_SNAKE_CASE										=   num_train_timesteps // self.num_inference_steps
           # creates integer timesteps by multiplying by ratio
           # casting to int to avoid issues when num_inference_step is power of 3
           SCREAMING_SNAKE_CASE										=   (np.arange(0     , UpperCamelCase__			) * step_ratio).round()[::-1].copy().astype(UpperCamelCase__			)
           timesteps += self.config.steps_offset
       elif self.config.timestep_spacing == "trailing":
           SCREAMING_SNAKE_CASE										=   num_train_timesteps / self.num_inference_steps
           # creates integer timesteps by multiplying by ratio
           # casting to int to avoid issues when num_inference_step is power of 3
           SCREAMING_SNAKE_CASE										=   (np.arange(UpperCamelCase__     , 0     , -step_ratio			)).round().copy().astype(UpperCamelCase__			)
           timesteps -= 1
       else:
           raise ValueError(
               f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'."			)

       SCREAMING_SNAKE_CASE										=   np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
       SCREAMING_SNAKE_CASE										=   torch.from_numpy(np.log(UpperCamelCase__			)			).to(UpperCamelCase__			)

       SCREAMING_SNAKE_CASE										=   np.interp(UpperCamelCase__     , np.arange(0     , len(UpperCamelCase__			)			)     , UpperCamelCase__			)
       SCREAMING_SNAKE_CASE										=   np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
       SCREAMING_SNAKE_CASE										=   torch.from_numpy(UpperCamelCase__			).to(device=UpperCamelCase__			)

       # interpolate sigmas
       SCREAMING_SNAKE_CASE										=   sigmas.log().lerp(sigmas.roll(1			).log()     , 0.5			).exp()

       SCREAMING_SNAKE_CASE										=   torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2			), sigmas[-1:]]			)
       SCREAMING_SNAKE_CASE										=   torch.cat(
           [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2			), sigmas_interpol[-1:]]			)

       if str(UpperCamelCase__			).startswith("mps"			):
           # mps does not support float64
           SCREAMING_SNAKE_CASE										=   torch.from_numpy(UpperCamelCase__			).to(UpperCamelCase__     , dtype=torch.floataa			)
       else:
           SCREAMING_SNAKE_CASE										=   torch.from_numpy(UpperCamelCase__			).to(UpperCamelCase__			)

       # interpolate timesteps
       SCREAMING_SNAKE_CASE										=   self.sigma_to_t(UpperCamelCase__			).to(UpperCamelCase__     , dtype=timesteps.dtype			)
       SCREAMING_SNAKE_CASE										=   torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])     , dim=-1			).flatten()

       SCREAMING_SNAKE_CASE										=   torch.cat([timesteps[:1], interleaved_timesteps]			)

       SCREAMING_SNAKE_CASE										=   None

       # for exp beta schedules, such as the one for `pipeline_shap_e.py`
       # we need an index counter
       SCREAMING_SNAKE_CASE										=   defaultdict(UpperCamelCase__			)





   def      _snake_case		(       self					:			Tuple     , __lowerCamelCase					:			Dict			):
       SCREAMING_SNAKE_CASE										=   sigma.log()

       # get distribution
       SCREAMING_SNAKE_CASE										=   log_sigma - self.log_sigmas[:, None]

       # get sigmas range
       SCREAMING_SNAKE_CASE										=   dists.ge(0			).cumsum(dim=0			).argmax(dim=0			).clamp(max=self.log_sigmas.shape[0] - 2			)
       SCREAMING_SNAKE_CASE										=   low_idx + 1

       SCREAMING_SNAKE_CASE										=   self.log_sigmas[low_idx]
       SCREAMING_SNAKE_CASE										=   self.log_sigmas[high_idx]

       # interpolate sigmas
       SCREAMING_SNAKE_CASE										=   (low - log_sigma) / (low - high)
       SCREAMING_SNAKE_CASE										=   w.clamp(0     , 1			)

       # transform interpolation to time range
       SCREAMING_SNAKE_CASE										=   (1 - w) * low_idx + w * high_idx
       SCREAMING_SNAKE_CASE										=   t.view(sigma.shape			)
       return t





   @property
   def      _snake_case		(       self					:			Any			):
       return self.sample is None





   def      _snake_case		(       self					:			Union[str, Any]     , __lowerCamelCase					:			Union[torch.FloatTensor, np.ndarray]     , __lowerCamelCase					:			Union[float, torch.FloatTensor]     , __lowerCamelCase					:			Union[torch.FloatTensor, np.ndarray]     , __lowerCamelCase					:			bool = True     , ):
       SCREAMING_SNAKE_CASE										=   self.index_for_timestep(UpperCamelCase__			)

       # advance index counter by 1
       SCREAMING_SNAKE_CASE										=   timestep.cpu().item() if torch.is_tensor(UpperCamelCase__			) else timestep
       self._index_counter[timestep_int] += 1

       if self.state_in_first_order:
           SCREAMING_SNAKE_CASE										=   self.sigmas[step_index]
           SCREAMING_SNAKE_CASE										=   self.sigmas_interpol[step_index + 1]
           SCREAMING_SNAKE_CASE										=   self.sigmas[step_index + 1]
       else:
           # 2nd order / KDPM2's method
           SCREAMING_SNAKE_CASE										=   self.sigmas[step_index - 1]
           SCREAMING_SNAKE_CASE										=   self.sigmas_interpol[step_index]
           SCREAMING_SNAKE_CASE										=   self.sigmas[step_index]

       # currently only gamma=0 is supported. This usually works best anyways.
       # We can support gamma in the future but then need to scale the timestep before
       # passing it to the model which requires a change in API
       SCREAMING_SNAKE_CASE										=   0
       SCREAMING_SNAKE_CASE										=   sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
           SCREAMING_SNAKE_CASE										=   sigma_hat if self.state_in_first_order else sigma_interpol
           SCREAMING_SNAKE_CASE										=   sample - sigma_input * model_output
       elif self.config.prediction_type == "v_prediction":
           SCREAMING_SNAKE_CASE										=   sigma_hat if self.state_in_first_order else sigma_interpol
           SCREAMING_SNAKE_CASE										=   model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
               sample / (sigma_input**2 + 1)
           )
       elif self.config.prediction_type == "sample":
           raise NotImplementedError("prediction_type not implemented yet: sample"			)
       else:
           raise ValueError(
               f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"			)

       if self.state_in_first_order:
           # 2. Convert to an ODE derivative for 1st order
           SCREAMING_SNAKE_CASE										=   (sample - pred_original_sample) / sigma_hat
           # 3. delta timestep
           SCREAMING_SNAKE_CASE										=   sigma_interpol - sigma_hat

           # store for 2nd order step
           SCREAMING_SNAKE_CASE										=   sample
       else:
           # DPM-Solver-2
           # 2. Convert to an ODE derivative for 2nd order
           SCREAMING_SNAKE_CASE										=   (sample - pred_original_sample) / sigma_interpol

           # 3. delta timestep
           SCREAMING_SNAKE_CASE										=   sigma_next - sigma_hat

           SCREAMING_SNAKE_CASE										=   self.sample
           SCREAMING_SNAKE_CASE										=   None

       SCREAMING_SNAKE_CASE										=   sample + derivative * dt

       if not return_dict:
           return (prev_sample,)

       return SchedulerOutput(prev_sample=UpperCamelCase__			)





   def      _snake_case		(       self					:			Optional[Any]     , __lowerCamelCase					:			torch.FloatTensor     , __lowerCamelCase					:			torch.FloatTensor     , __lowerCamelCase					:			torch.FloatTensor     , ):
       SCREAMING_SNAKE_CASE										=   self.sigmas.to(device=original_samples.device     , dtype=original_samples.dtype			)
       if original_samples.device.type == "mps" and torch.is_floating_point(UpperCamelCase__			):
           # mps does not support float64
           SCREAMING_SNAKE_CASE										=   self.timesteps.to(original_samples.device     , dtype=torch.floataa			)
           SCREAMING_SNAKE_CASE										=   timesteps.to(original_samples.device     , dtype=torch.floataa			)
       else:
           SCREAMING_SNAKE_CASE										=   self.timesteps.to(original_samples.device			)
           SCREAMING_SNAKE_CASE										=   timesteps.to(original_samples.device			)

       SCREAMING_SNAKE_CASE										=   [self.index_for_timestep(UpperCamelCase__     , UpperCamelCase__			) for t in timesteps]

       SCREAMING_SNAKE_CASE										=   sigmas[step_indices].flatten()
       while len(sigma.shape			) < len(original_samples.shape			):
           SCREAMING_SNAKE_CASE										=   sigma.unsqueeze(-1			)

       SCREAMING_SNAKE_CASE										=   original_samples + noise * sigma
       return noisy_samples





   def __len__(       self					:			Union[str, Any]			):
       return self.config.num_train_timesteps

from __future__ import annotations

def a__       (			A_,	A_   ):






  '''simple docstring'''





  if b == 0:
    return (1, 0)
  ((__magic_name__)	,       (__magic_name__))								=			extended_euclid(A_,	a % b   )
  __magic_name__								=			a // b
  return (y, x - k * y)

def a__       (			A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  ((__magic_name__)	,       (__magic_name__))								=			extended_euclid(A_,	A_   )
  __magic_name__								=			na * na
  __magic_name__								=			ra * x * na + ra * y * na
  return (n % m + m) % m

def a__       (			A_,	A_   ):






  '''simple docstring'''





  ((__magic_name__)	,       (__magic_name__))								=			extended_euclid(A_,	A_   )
  if b < 0:
    __magic_name__								=			(b % n + n) % n
  return b

def a__       (			A_,	A_,	A_,	A_   ):






  '''simple docstring'''





  __magic_name__	,       __magic_name__								=			invert_modulo(A_,	A_   ), invert_modulo(A_,	A_   )
  __magic_name__								=			na * na
  __magic_name__								=			ra * x * na + ra * y * na
  return (n % m + m) % m


if __name__ == "__main__":
    from doctest import testmod

    testmod(name='chinese_remainder_theorem', verbose=True)
    testmod(name='chinese_remainder_theorem2', verbose=True)
    testmod(name='invert_modulo', verbose=True)
    testmod(name='extended_euclid', verbose=True)

